In this activity, students compare two groups using data from samples but do not initially have enough information to do so. To bridge the gap, they need to exchange questions and ideas.

The Info Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

After students have completed their work, share the correct answers, and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “What was the most important question you asked for the first problem? For the second problem?”
• “What are some other ways the information could have been given to solve the problems?” (Instead of the characteristics for the first question, a box plot could have been presented. The second question could have had a dot plot or characteristics like the first problem.)
• “If the distributions for the first problem had been symmetric, would the answer have been the same?” (Yes. The difference in means is 34.25, which is only 1.6 MADs apart, so there would not have been enough information to say that the two population means are meaningfully different.)

Highlight for students that it is important to have measures of center as well as measures of variability when comparing groups.

Invite 2–3 students to share the norm they chose and how it supported the work of the group or a realization they had about a norm that would have worked better in this situation. Provide these sentence frames to help students organize their thoughts in a clear, precise way:

• “I picked the norm ‘.’ It really helped me/my group because ​.”
• “I picked the norm ‘.’ During the activity, I realized the norm ‘​’ would be a better focus because .”

In this activity, students compare two populations using samples again, but this time only one sample is given. For the other sample, the characteristics have either been computed already or are the focus of the question. This type of analysis is useful when comparing two similar populations as in this activity or when comparing a group against a standard.

The purpose of the discussion is to help students understand how to compare groups when one set of characteristics are known and the other group is represented by sample data.

Select some groups to share their answers and reasoning for the two problems. 

Consider asking these discussion questions:

• “How did you determine what to use as a typical value for the first problem?” (Since there is one value much greater than the others, the distribution is not symmetric, so median is a more appropriate measure of center.)
• “How did you determine what measure of center to use for the second problem?” (Since the data are all close, either value could be used, but the new equipment reported the “average,” or mean, so the mean should be used for the sample as well.)
• “The manufacturer for the new equipment guarantees 4 flaws or fewer per day with the new equipment. If the new equipment produces only 3 flaws per day, does that change the answer for the second problem?” (No. There is an even greater difference between the current and new equipment, so it is even more meaningful.)
• “What other factors would the college graduate want to consider other than the meaningful difference in median salary between the two companies?” (He should consider other factors such as benefits, relationship with coworkers, type of work being done at each company, and so on. The graduate should consider the salary for the type of job he will get at the company. For example, if his degree is in computer science, he may be looking at a job with computers rather than sales or some other department within the company, so he might be able to get a better comparison of salaries that way.)
• “What other factors would the factory manager want to consider other than the meaningful difference in flaws for the equipment?” (The cost of the frequent flaws as well as the cost of the new equipment will probably factor into her decision to buy new equipment. The age of the current equipment and maintenance for older equipment compared to new equipment may also be important.)